Question

A 1-kg ball is released from a height of 6 m, and a 2-kg ball is released from a height of 3 m. Air resistance is negligible as they fall. Which of the following statements about these balls are correct?

A) Both balls will reach the ground with the same kinetic energy.
B) Both balls will reach the ground with the same speed.
C) As they reach the ground, the 1-kg ball will be moving faster than the 2-kg ball.
D) As they reach the ground, the 1-kg ball will have more kinetic energy than the 2-kg ball because it was dropped from a greater height.
E) Both balls will take the same time to reach the ground.

Answer 1

A) True B) false C) True D) False E) False

Step-by-step explanation:

A) We know that the potential energy is transformed into kinetic energy since the ball is released.

`EP1=m*g*h = 1 * 9.81 * 6 = 58.86J\\`

This energy will be the same at the moment that the ball is about to hit the floor. Therefore there was a transformation from potential to kinetic energy

EK1 = EP1

`EK=(1)/(2)*m*v^(2)  \\v1=√((58.86*2)/1) \\v1=10,84 m/s`

With the 2kg ball happens the same

`EP2=m*g*h2=2*9.81*3=58.86J\\`

Velocity at the moment when is about to hit the floor (due to the energy transform) will be:

`EK2=(1)/(2)*m*v^(2)  \\v1=√((58.86*2)/2) \\v2=7.67 m/s`

A) Since both balls have the same potential energy, they will have the same kinetic energy

B) The velocities are differents as they were calculated before.

C) Therefore the 1 kg ball moves faster as it reaches the ground.

D) The kinetic energy is the same for both balls as it was calculated before.

E) The 2 kg ball will reach the ground first, since it is closer to the ground

With the velocities calculated in the previous steps we have now:

`1 kg ball\\v=v0+g*t\\t1=10.85/9.81 = 1.1s\\\\2 kg ball\\t2=7.672/9.81 = 0.782s`